OK, this is really beginning to feel like a problem with the exchange. I just tried to make a phone call, and while I was on hold and listening to terrible music at a terrible quality, the call went dead exactly at the same time as the ping command I had running stopped receiving replies. However, while the internet connection is down, the ADSL line itself is up according to my router, and I do get a dial tone.
So,
1) I get absolutely no data packets from the other end when the internet connection is down
2) My ADSL line is still up while the internet connection is down
3) I do get a dial tone if I pick up the phone, but
4) Calls do not work while the internet connection is down.
Smells like an exchange problem to me. What do you think?